diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/KBigInteger.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/KBigInteger.kt index 036f44a91..b9b2bbb81 100644 --- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/KBigInteger.kt +++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/KBigInteger.kt @@ -26,45 +26,256 @@ object KBigIntegerRing: Ring { override fun multiply(a: KBigInteger, b: KBigInteger): KBigInteger = a.times(b) - operator fun String.unaryPlus(): KBigInteger = KBigInteger(this)!! + operator fun String.unaryPlus(): KBigInteger = this.toKBigInteger()!! - operator fun String.unaryMinus(): KBigInteger = -KBigInteger(this)!! + operator fun String.unaryMinus(): KBigInteger = -this.toKBigInteger()!! } - @kotlin.ExperimentalUnsignedTypes -class KBigInteger(sign: Int = 0, magnitude: Magnitude = Magnitude(0)): - RingElement, Comparable { +class KBigInteger internal constructor( + private val sign: Byte = 0, + private val magnitude: Magnitude = Magnitude(0) +): Comparable { - constructor(x: Int) : this(x.sign, uintArrayOf(kotlin.math.abs(x).toUInt())) - constructor(x: Long) : this(x.sign, uintArrayOf( + constructor(x: Int) : this(x.sign.toByte(), uintArrayOf(kotlin.math.abs(x).toUInt())) + + constructor(x: Long) : this(x.sign.toByte(), stripLeadingZeros(uintArrayOf( (kotlin.math.abs(x).toULong() and BASE).toUInt(), - ((kotlin.math.abs(x).toULong() shr BASE_SIZE) and BASE).toUInt())) + ((kotlin.math.abs(x).toULong() shr BASE_SIZE) and BASE).toUInt()))) - val magnitude = stripLeadingZeros(magnitude) - val sign = if (this.magnitude.isNotEmpty()) sign else 0 - val sizeByte: Int = magnitude.size * BASE_SIZE / 4 + override fun compareTo(other: KBigInteger): Int { + return when { + (this.sign == 0.toByte()) and (other.sign == 0.toByte()) -> 0 + this.sign < other.sign -> -1 + this.sign > other.sign -> 1 + else -> this.sign * compareMagnitudes(this.magnitude, other.magnitude) + } + } - override val context: KBigIntegerRing get() = KBigIntegerRing + override fun equals(other: Any?): Boolean { + if (other is KBigInteger) { + return this.compareTo(other) == 0 + } + else error("Can't compare KBigInteger to a different type") + } - override fun unwrap(): KBigInteger = this - override fun KBigInteger.wrap(): KBigInteger = this + override fun hashCode(): Int { + return magnitude.hashCode() + this.sign + } + + fun abs(): KBigInteger = if (sign == 0.toByte()) this else KBigInteger(1, magnitude) + + operator fun unaryMinus(): KBigInteger { + return if (this.sign == 0.toByte()) this else KBigInteger((-this.sign).toByte(), this.magnitude) + } + + operator fun plus(b: KBigInteger): KBigInteger { + return when { + b.sign == 0.toByte() -> this + this.sign == 0.toByte() -> b + this == -b -> ZERO + this.sign == b.sign -> KBigInteger(this.sign, addMagnitudes(this.magnitude, b.magnitude)) + else -> { + val comp: Int = compareMagnitudes(this.magnitude, b.magnitude) + + if (comp == 1) { + KBigInteger(this.sign, subtractMagnitudes(this.magnitude, b.magnitude)) + } else { + KBigInteger((-this.sign).toByte(), subtractMagnitudes(b.magnitude, this.magnitude)) + } + } + } + } + + operator fun minus(b: KBigInteger): KBigInteger { + return this + (-b) + } + + operator fun times(b: KBigInteger): KBigInteger { + return when { + this.sign == 0.toByte() -> ZERO + b.sign == 0.toByte() -> ZERO +// TODO: Karatsuba + else -> KBigInteger((this.sign * b.sign).toByte(), multiplyMagnitudes(this.magnitude, b.magnitude)) + } + } + + operator fun times(other: UInt): KBigInteger { + return when { + this.sign == 0.toByte() -> ZERO + other == 0U -> ZERO + else -> KBigInteger(this.sign, multiplyMagnitudeByUInt(this.magnitude, other)) + } + } + + operator fun times(other: Int): KBigInteger { + return if (other > 0) + this * kotlin.math.abs(other).toUInt() + else + -this * kotlin.math.abs(other).toUInt() + } + + operator fun div(other: UInt): KBigInteger { + return KBigInteger(this.sign, divideMagnitudeByUInt(this.magnitude, other)) + } + + operator fun div(other: Int): KBigInteger { + return KBigInteger((this.sign * other.sign).toByte(), + divideMagnitudeByUInt(this.magnitude, kotlin.math.abs(other).toUInt())) + } + + private fun division(other: KBigInteger): Pair { + // Long division algorithm: + // https://en.wikipedia.org/wiki/Division_algorithm#Integer_division_(unsigned)_with_remainder + // TODO: Implement more effective algorithm + var q: KBigInteger = ZERO + var r: KBigInteger = ZERO + + val bitSize = (BASE_SIZE * (this.magnitude.size - 1) + log2(this.magnitude.last().toFloat() + 1)).toInt() + for (i in bitSize downTo 0) { + r = r shl 1 + r = r or ((abs(this) shr i) and ONE) + if (r >= abs(other)) { + r -= abs(other) + q += (ONE shl i) + } + } + + return Pair(KBigInteger((this.sign * other.sign).toByte(), q.magnitude), r) + } + + operator fun div(other: KBigInteger): KBigInteger { + return this.division(other).first + } + + infix fun shl(i: Int): KBigInteger { + if (this == ZERO) return ZERO + if (i == 0) return this + + val fullShifts = i / BASE_SIZE + 1 + val relShift = i % BASE_SIZE + val shiftLeft = {x: UInt -> if (relShift >= 32) 0U else x shl relShift} + val shiftRight = {x: UInt -> if (BASE_SIZE - relShift >= 32) 0U else x shr (BASE_SIZE - relShift)} + + val newMagnitude: Magnitude = Magnitude(this.magnitude.size + fullShifts) + + for (j in this.magnitude.indices) { + newMagnitude[j + fullShifts - 1] = shiftLeft(this.magnitude[j]) + if (j != 0) { + newMagnitude[j + fullShifts - 1] = newMagnitude[j + fullShifts - 1] or shiftRight(this.magnitude[j - 1]) + } + } + + newMagnitude[this.magnitude.size + fullShifts - 1] = shiftRight(this.magnitude.last()) + + return KBigInteger(this.sign, stripLeadingZeros(newMagnitude)) + } + + infix fun shr(i: Int): KBigInteger { + if (this == ZERO) return ZERO + if (i == 0) return this + + val fullShifts = i / BASE_SIZE + val relShift = i % BASE_SIZE + val shiftRight = {x: UInt -> if (relShift >= 32) 0U else x shr relShift} + val shiftLeft = {x: UInt -> if (BASE_SIZE - relShift >= 32) 0U else x shl (BASE_SIZE - relShift)} + if (this.magnitude.size - fullShifts <= 0) { + return ZERO + } + val newMagnitude: Magnitude = Magnitude(this.magnitude.size - fullShifts) + + for (j in fullShifts until this.magnitude.size) { + newMagnitude[j - fullShifts] = shiftRight(this.magnitude[j]) + if (j != this.magnitude.size - 1) { + newMagnitude[j - fullShifts] = newMagnitude[j - fullShifts] or shiftLeft(this.magnitude[j + 1]) + } + } + + return KBigInteger(this.sign, stripLeadingZeros(newMagnitude)) + } + + infix fun or(other: KBigInteger): KBigInteger { + if (this == ZERO) return other; + if (other == ZERO) return this; + val resSize = max(this.magnitude.size, other.magnitude.size) + val newMagnitude: Magnitude = Magnitude(resSize) + for (i in 0 until resSize) { + if (i < this.magnitude.size) { + newMagnitude[i] = newMagnitude[i] or this.magnitude[i] + } + if (i < other.magnitude.size) { + newMagnitude[i] = newMagnitude[i] or other.magnitude[i] + } + } + return KBigInteger(1, stripLeadingZeros(newMagnitude)) + } + + infix fun and(other: KBigInteger): KBigInteger { + if ((this == ZERO) or (other == ZERO)) return ZERO; + val resSize = min(this.magnitude.size, other.magnitude.size) + val newMagnitude: Magnitude = Magnitude(resSize) + for (i in 0 until resSize) { + newMagnitude[i] = this.magnitude[i] and other.magnitude[i] + } + return KBigInteger(1, stripLeadingZeros(newMagnitude)) + } + + operator fun rem(other: Int): Int { + val res = this - (this / other) * other + return if (res == ZERO) 0 else res.sign * res.magnitude[0].toInt() + } + + operator fun rem(other: KBigInteger): KBigInteger { + return this - (this / other) * other + } + + fun modPow(exponent: KBigInteger, m: KBigInteger): KBigInteger { + return when { + exponent == ZERO -> ONE + exponent % 2 == 1 -> (this * modPow(exponent - ONE, m)) % m + else -> { + val sqRoot = modPow(exponent / 2, m) + (sqRoot * sqRoot) % m + } + } + } + + override fun toString(): String { + if (this.sign == 0.toByte()) { + return "0x0" + } + var res: String = if (this.sign == (-1).toByte()) "-0x" else "0x" + var numberStarted = false + + for (i in this.magnitude.size - 1 downTo 0) { + for (j in BASE_SIZE / 4 - 1 downTo 0) { + val curByte = (this.magnitude[i] shr 4 * j) and 0xfU + if (numberStarted or (curByte != 0U)) { + numberStarted = true + res += hexMapping[curByte] + } + } + } + + return res + } companion object { - val BASE = 0xffffffffUL + const val BASE = 0xffffffffUL const val BASE_SIZE: Int = 32 val ZERO: KBigInteger = KBigInteger() val ONE: KBigInteger = KBigInteger(1) private val hexMapping: HashMap = hashMapOf( - 0U to "0", 1U to "1", 2U to "2", 3U to "3", 4U to "4", 5U to "5", 6U to "6", 7U to "7", 8U to "8", - 9U to "9", 10U to "a", 11U to "b", 12U to "c", 13U to "d", 14U to "e", 15U to "f" + 0U to "0", 1U to "1", 2U to "2", 3U to "3", + 4U to "4", 5U to "5", 6U to "6", 7U to "7", + 8U to "8", 9U to "9", 10U to "a", 11U to "b", + 12U to "c", 13U to "d", 14U to "e", 15U to "f" ) - private fun stripLeadingZeros(mag: Magnitude): Magnitude { - // TODO: optimize performance - if (mag.isEmpty()) { + internal fun stripLeadingZeros(mag: Magnitude): Magnitude { + if (mag.isEmpty() || mag.last() != 0U) { return mag } var resSize: Int = mag.size - 1 @@ -108,7 +319,7 @@ class KBigInteger(sign: Int = 0, magnitude: Magnitude = Magnitude(0)): carry = (res shr BASE_SIZE) } result[resultLength - 1] = carry.toUInt() - return result + return stripLeadingZeros(result) } private fun subtractMagnitudes(mag1: Magnitude, mag2: Magnitude): Magnitude { @@ -127,7 +338,7 @@ class KBigInteger(sign: Int = 0, magnitude: Magnitude = Magnitude(0)): result[i] = res.toUInt() } - return result + return stripLeadingZeros(result) } private fun multiplyMagnitudeByUInt(mag: Magnitude, x: UInt): Magnitude { @@ -142,7 +353,7 @@ class KBigInteger(sign: Int = 0, magnitude: Magnitude = Magnitude(0)): } result[resultLength - 1] = (carry and BASE).toUInt() - return result + return stripLeadingZeros(result) } private fun multiplyMagnitudes(mag1: Magnitude, mag2: Magnitude): Magnitude { @@ -159,7 +370,7 @@ class KBigInteger(sign: Int = 0, magnitude: Magnitude = Magnitude(0)): result[i + mag2.size] = (carry and BASE).toUInt() } - return result + return stripLeadingZeros(result) } private fun divideMagnitudeByUInt(mag: Magnitude, x: UInt): Magnitude { @@ -172,230 +383,15 @@ class KBigInteger(sign: Int = 0, magnitude: Magnitude = Magnitude(0)): result[i] = (cur / x).toUInt() carry = cur % x } - return result + return stripLeadingZeros(result) } } - override fun compareTo(other: KBigInteger): Int { - return when { - (this.sign == 0) and (other.sign == 0) -> 0 - this.sign < other.sign -> -1 - this.sign > other.sign -> 1 - else -> this.sign * compareMagnitudes(this.magnitude, other.magnitude) - } - } - - override fun equals(other: Any?): Boolean { - if (other is KBigInteger) { - return this.compareTo(other) == 0 - } - else error("Can't compare KBigInteger to a different type") - } - - override fun hashCode(): Int { - return magnitude.hashCode() + this.sign - } - - operator fun unaryMinus(): KBigInteger { - return if (this.sign == 0) this else KBigInteger(-this.sign, this.magnitude) - } - - override operator fun plus(b: KBigInteger): KBigInteger { - return when { - b.sign == 0 -> this - this.sign == 0 -> b - this == -b -> ZERO - this.sign == b.sign -> KBigInteger(this.sign, addMagnitudes(this.magnitude, b.magnitude)) - else -> { - val comp: Int = compareMagnitudes(this.magnitude, b.magnitude) - - if (comp == 1) { - KBigInteger(this.sign, subtractMagnitudes(this.magnitude, b.magnitude)) - } else { - KBigInteger(-this.sign, subtractMagnitudes(b.magnitude, this.magnitude)) - } - } - } - } - - override operator fun minus(b: KBigInteger): KBigInteger { - return this + (-b) - } - - override operator fun times(b: KBigInteger): KBigInteger { - return when { - this.sign == 0 -> ZERO - b.sign == 0 -> ZERO -// TODO: Karatsuba - else -> KBigInteger(this.sign * b.sign, multiplyMagnitudes(this.magnitude, b.magnitude)) - } - } - - operator fun times(other: UInt): KBigInteger { - return when { - this.sign == 0 -> ZERO - other == 0U -> ZERO - else -> KBigInteger(this.sign, multiplyMagnitudeByUInt(this.magnitude, other)) - } - } - - operator fun times(other: Int): KBigInteger { - return if (other > 0) - this * kotlin.math.abs(other).toUInt() - else - -this * kotlin.math.abs(other).toUInt() - } - - operator fun div(other: UInt): KBigInteger { - return KBigInteger(this.sign, divideMagnitudeByUInt(this.magnitude, other)) - } - - operator fun div(other: Int): KBigInteger { - return KBigInteger(this.sign * other.sign, divideMagnitudeByUInt(this.magnitude, kotlin.math.abs(other).toUInt())) - } - - private fun division(other: KBigInteger): Pair { - // Long division algorithm: - // https://en.wikipedia.org/wiki/Division_algorithm#Integer_division_(unsigned)_with_remainder - // TODO: Implement more effective algorithm - var q: KBigInteger = ZERO - var r: KBigInteger = ZERO - - val bitSize = (BASE_SIZE * (this.magnitude.size - 1) + log2(this.magnitude.last().toFloat() + 1)).toInt() - for (i in bitSize downTo 0) { - r = r shl 1 - r = r or ((abs(this) shr i) and ONE) - if (r >= abs(other)) { - r -= abs(other) - q += (ONE shl i) - } - } - - return Pair(KBigInteger(this.sign * other.sign, q.magnitude), r) - } - - operator fun div(other: KBigInteger): KBigInteger { - return this.division(other).first - } - - infix fun shl(i: Int): KBigInteger { - if (this == ZERO) return ZERO - if (i == 0) return this - - val fullShifts = i / BASE_SIZE + 1 - val relShift = i % BASE_SIZE - val shiftLeft = {x: UInt -> if (relShift >= 32) 0U else x shl relShift} - val shiftRight = {x: UInt -> if (BASE_SIZE - relShift >= 32) 0U else x shr (BASE_SIZE - relShift)} - - val newMagnitude: Magnitude = Magnitude(this.magnitude.size + fullShifts) - - for (j in this.magnitude.indices) { - newMagnitude[j + fullShifts - 1] = shiftLeft(this.magnitude[j]) - if (j != 0) { - newMagnitude[j + fullShifts - 1] = newMagnitude[j + fullShifts - 1] or shiftRight(this.magnitude[j - 1]) - } - } - - newMagnitude[this.magnitude.size + fullShifts - 1] = shiftRight(this.magnitude.last()) - - return KBigInteger(this.sign, newMagnitude) - } - - infix fun shr(i: Int): KBigInteger { - if (this == ZERO) return ZERO - if (i == 0) return this - - val fullShifts = i / BASE_SIZE - val relShift = i % BASE_SIZE - val shiftRight = {x: UInt -> if (relShift >= 32) 0U else x shr relShift} - val shiftLeft = {x: UInt -> if (BASE_SIZE - relShift >= 32) 0U else x shl (BASE_SIZE - relShift)} - if (this.magnitude.size - fullShifts <= 0) { - return ZERO - } - val newMagnitude: Magnitude = Magnitude(this.magnitude.size - fullShifts) - - for (j in fullShifts until this.magnitude.size) { - newMagnitude[j - fullShifts] = shiftRight(this.magnitude[j]) - if (j != this.magnitude.size - 1) { - newMagnitude[j - fullShifts] = newMagnitude[j - fullShifts] or shiftLeft(this.magnitude[j + 1]) - } - } - - return KBigInteger(this.sign, newMagnitude) - } - - infix fun or(other: KBigInteger): KBigInteger { - if (this == ZERO) return other; - if (other == ZERO) return this; - val resSize = max(this.magnitude.size, other.magnitude.size) - val newMagnitude: Magnitude = Magnitude(resSize) - for (i in 0 until resSize) { - if (i < this.magnitude.size) { - newMagnitude[i] = newMagnitude[i] or this.magnitude[i] - } - if (i < other.magnitude.size) { - newMagnitude[i] = newMagnitude[i] or other.magnitude[i] - } - } - return KBigInteger(1, newMagnitude) - } - - infix fun and(other: KBigInteger): KBigInteger { - if ((this == ZERO) or (other == ZERO)) return ZERO; - val resSize = min(this.magnitude.size, other.magnitude.size) - val newMagnitude: Magnitude = Magnitude(resSize) - for (i in 0 until resSize) { - newMagnitude[i] = this.magnitude[i] and other.magnitude[i] - } - return KBigInteger(1, newMagnitude) - } - - operator fun rem(other: Int): Int { - val res = this - (this / other) * other - return if (res == ZERO) 0 else res.sign * res.magnitude[0].toInt() - } - - operator fun rem(other: KBigInteger): KBigInteger { - return this - (this / other) * other - } - - fun modPow(exponent: KBigInteger, m: KBigInteger): KBigInteger { - return when { - exponent == ZERO -> ONE - exponent % 2 == 1 -> (this * modPow(exponent - ONE, m)) % m - else -> { - val sqRoot = modPow(exponent / 2, m) - (sqRoot * sqRoot) % m - } - } - } - - override fun toString(): String { - if (this.sign == 0) { - return "0x0" - } - var res: String = if (this.sign == -1) "-0x" else "0x" - var numberStarted = false - - for (i in this.magnitude.size - 1 downTo 0) { - for (j in BASE_SIZE / 4 - 1 downTo 0) { - val curByte = (this.magnitude[i] shr 4 * j) and 0xfU - if (numberStarted or (curByte != 0U)) { - numberStarted = true - res += hexMapping[curByte] - } - } - } - - return res - } } @kotlin.ExperimentalUnsignedTypes -fun abs(x: KBigInteger): KBigInteger { - return if (x.sign == 0) x else KBigInteger(1, x.magnitude) -} +fun abs(x: KBigInteger): KBigInteger = x.abs() @kotlin.ExperimentalUnsignedTypes // Can't put it as constructor in class due to platform declaration clash with KBigInteger(Int) @@ -405,26 +401,35 @@ fun KBigInteger(x: UInt): KBigInteger @kotlin.ExperimentalUnsignedTypes // Can't put it as constructor in class due to platform declaration clash with KBigInteger(Long) fun KBigInteger(x: ULong): KBigInteger - = KBigInteger(1, uintArrayOf((x and KBigInteger.BASE).toUInt(), ((x shr KBigInteger.BASE_SIZE) and KBigInteger.BASE).toUInt())) + = KBigInteger(1, + KBigInteger.stripLeadingZeros(uintArrayOf( + (x and KBigInteger.BASE).toUInt(), + ((x shr KBigInteger.BASE_SIZE) and KBigInteger.BASE).toUInt()) + ) + ) -val hexChToInt = hashMapOf('0' to 0, '1' to 1, '2' to 2, '3' to 3, '4' to 4, '5' to 5, '6' to 6, '7' to 7, - '8' to 8, '9' to 9, 'A' to 10, 'B' to 11, 'C' to 12, 'D' to 13, 'E' to 14, 'F' to 15) +val hexChToInt = hashMapOf( + '0' to 0, '1' to 1, '2' to 2, '3' to 3, + '4' to 4, '5' to 5, '6' to 6, '7' to 7, + '8' to 8, '9' to 9, 'A' to 10, 'B' to 11, + 'C' to 12, 'D' to 13, 'E' to 14, 'F' to 15 +) // Returns None if a valid number can not be read from a string -fun KBigInteger(s: String): KBigInteger? { +fun String.toKBigInteger(): KBigInteger? { val sign: Int val sPositive: String when { - s[0] == '+' -> { + this[0] == '+' -> { sign = +1 - sPositive = s.substring(1) + sPositive = this.substring(1) } - s[0] == '-' -> { + this[0] == '-' -> { sign = -1 - sPositive = s.substring(1) + sPositive = this.substring(1) } else -> { - sPositive = s + sPositive = this sign = +1 } } diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/KBigIntegerTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/KBigIntegerTest.kt index daece0f45..96e2dee9a 100644 --- a/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/KBigIntegerTest.kt +++ b/kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/KBigIntegerTest.kt @@ -485,13 +485,13 @@ class KBigIntegerConversionsTest { @Test fun testFromString_0x17ead2ffffd11223344() { - val x = KBigInteger("0x17ead2ffffd11223344")!! + val x = "0x17ead2ffffd11223344".toKBigInteger() assertEquals( "0x17ead2ffffd11223344", x.toString()) } @Test fun testFromString_7059135710711894913860() { - val x = KBigInteger("-7059135710711894913860") + val x = "-7059135710711894913860".toKBigInteger() assertEquals("-0x17ead2ffffd11223344", x.toString()) } } @@ -509,7 +509,7 @@ class KBigIntegerRingTest { fun testKBigIntegerRingSum_100_000_000__100_000_000() { KBigIntegerRing { val sum = +"100_000_000" + +"100_000_000" - assertEquals(sum, KBigInteger("200_000_000")) + assertEquals(sum, "200_000_000".toKBigInteger()) } } @@ -517,7 +517,7 @@ class KBigIntegerRingTest { fun test_mul_3__4() { KBigIntegerRing { val prod = +"0x3000_0000_0000" * +"0x4000_0000_0000_0000_0000" - assertEquals(prod, KBigInteger("0xc00_0000_0000_0000_0000_0000_0000_0000")) + assertEquals(prod, "0xc00_0000_0000_0000_0000_0000_0000_0000".toKBigInteger()) } }